{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graph Probability Density Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## To DO\n",
    "\n",
    "# Show how people generate z score table\n",
    "# Show other uses of z score table similar to how people use it for the\n",
    "# coursera class on it. \n",
    "\n",
    "# Explain how table works (if stuff works)\n",
    "\n",
    "# Show boxplot and explain how it works. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probability Density Functions (PDF) do NOT show you the probability of events but their probability density. This notebook will show you how you can use the PDF to find the probability for a given <b>range</b> of numbers. This is basically an explanation of why the graph below makes sense. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](images/NormalDistribution.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability density function of a normal distribution with a mean (insert mean symbol) and variance (insert variance symbol) is: (INSERT EQUATION HERE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability density function of a normal distribution with mean of 0 and variance of 1 is: <br>\n",
    "\n",
    "$$f(x) = \\frac{1}{\\sqrt{2\\pi}}e^{-x^{2}/2}$$\n",
    "\n",
    "We will stick with this definition for this tutorial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy.integrate as integrate\n",
    "import scipy.special as special\n",
    "from scipy.integrate import quad\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Polygon\n",
    "import pandas as pd\n",
    "np.set_printoptions(suppress=True)\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## For the blog post part. \n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "x = np.linspace(-3, 3, num = 100)\n",
    "\n",
    "constant = 1.0 / np.sqrt(2*np.pi)\n",
    "pdf_normal_distribution = constant * np.exp((-x**2) / 2.0)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5));\n",
    "ax.plot(x, pdf_normal_distribution);\n",
    "ax.set_ylim(0);\n",
    "ax.set_title('Normal Distribution', size = 20);\n",
    "ax.set_ylabel('Probability Density', size = 20);\n",
    "\n",
    "fig.savefig('images/NormalDistribution1.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Within 1 Standard Deviation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Math Expression</b> $$\\int_{-1}^{1}\\frac{1}{\\sqrt{2\\pi}}e^{-x^{2}/2}\\mathrm{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.682689492137086\n"
     ]
    }
   ],
   "source": [
    "# Make the PDF for the normal distribution a function\n",
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )\n",
    "\n",
    "# Integrate PDF from -1 to 1\n",
    "result, _ = quad(normalProbabilityDensity, -1, 1, limit = 1000)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = -1, 1 # integral limits\n",
    "\n",
    "x = np.linspace(-3, 3)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(-1, 1)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(0, .08, r\"$\\int_{-1}^{1} f(x)\\mathrm{d}x = $\" + \"{0:.1f}%\".format(result*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "ax.set_title(r'68% of Values are within 1 STD', fontsize = 24);\n",
    "ax.set_ylabel(r'Probability Density', fontsize = 18);\n",
    "\n",
    "fig.savefig('images/68_1_std.png', dpi = 1200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Within 2 Standard Deviations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Math Expression</b> $$\\int_{-2}^{2}\\frac{1}{\\sqrt{2\\pi}}e^{-x^{2}/2}\\mathrm{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9544997361036417\n"
     ]
    }
   ],
   "source": [
    "# Make the PDF for the normal distribution a function\n",
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )\n",
    "\n",
    "# Integrate PDF from -2 to 2\n",
    "result, _ = quad(normalProbabilityDensity, -2, 2, limit = 1000)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = -2, 2 # integral limits\n",
    "\n",
    "x = np.linspace(-3, 3)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(0, .08, r\"$\\int_{-2}^{2} f(x)\\mathrm{d}x = $\" + \"{0:.1f}%\".format(result*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "ax.set_title(r'95% of Values are within 2 STD', fontsize = 24);\n",
    "ax.set_ylabel(r'Probability Density', fontsize = 18);\n",
    "\n",
    "fig.savefig('images/95_2_std.png', dpi = 1200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Within 3 Standard Deviations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Math Expression</b> $$\\int_{-3}^{3}\\frac{1}{\\sqrt{2\\pi}}e^{-x^{2}/2}\\mathrm{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9973002039367399\n"
     ]
    }
   ],
   "source": [
    "# Make the PDF for the normal distribution a function\n",
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )\n",
    "\n",
    "# Integrate PDF from -3 to 3\n",
    "result, _ = quad(normalProbabilityDensity, -3, 3, limit = 1000)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = -3, 3 # integral limits\n",
    "\n",
    "x = np.linspace(-3, 3)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(0, .08, r\"$\\int_{-3}^{3} f(x)\\mathrm{d}x = $\" + \"{0:.1f}%\".format(result*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "ax.set_title(r'99.7% of Values are within 3 STD', fontsize = 24);\n",
    "ax.set_ylabel(r'Probability Density', fontsize = 18);\n",
    "\n",
    "fig.savefig('images/99_3_std.png', dpi = 1200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Negative Infinity to Positive Infinity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For any PDF, the area under the curve must be 1 (the probability of drawing any number from the function's range is always 1). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result, error = quad(normalProbabilityDensity, np.NINF, np.inf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999999997"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Result should be very close to 1\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This should really be -inf to positive inf, but graph can only be so big. \n",
    "# Currently it is plus or minus 4 std deviations \n",
    "a, b = -4, 4 # integral limits\n",
    "\n",
    "x = np.linspace(a, b)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(0, .08, r\"$\\int_{-\\infty}^{\\infty} f(x)\\mathrm{d}x = 1$\",\n",
    "         horizontalalignment='center', fontsize=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The area under the curve is 1. Lets break down the different parts of the graph. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean (0) to Mean + STD (1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Integrate normal distribution from 0 to 1\n",
    "result, error = quad(normalProbabilityDensity, 0, 1, limit = 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.341344746068543"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LL+CcO/rKIhK2gildhd3J9jf/8p1zzznnGgJ3A/cd47YvOedSnXOpycnJQUQSkVDKzMyk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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106a38b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This should really be -inf to positive inf, but graph can only be so big. \n",
    "# Currently it is plus or minus 5 std deviations \n",
    "a, b = 0, 1 # integral limits\n",
    "\n",
    "x = np.linspace(-4, 4)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(0, 1)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(0.5, .05, r'{0:.2f}%'.format(result*100),\n",
    "         horizontalalignment='center', fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Looking at Between 1 STD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result, _ = quad(normalProbabilityDensity, -1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.682689492137086"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nzuWiiy7yHUOkQHFxcZx++ul88803vqOIRBSVLpEwNH36dDp16uQ7hsgx9enT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\nh281TSn5aAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x150ce1f910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This should really be -inf to positive inf, but graph can only be so big. \n",
    "# Currently it is plus or minus 5 std deviations \n",
    "a, b = -1, 1 # integral limits\n",
    "\n",
    "x = np.linspace(-4, 4)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(-1, 1)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(0.0, .05, r'{0:.1f}%'.format(result*100),\n",
    "         horizontalalignment='center', fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (Mean + STD) to Mean + (2STD)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result, error = quad(normalProbabilityDensity, 1, 2, limit = 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.13590512198327784"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ztm0b5cqV8x0lptWrV49ly5bh3F/eLBCRCJFr6XLOZQA3Ae8DS4DJzrnFZna/mXUKDLvJ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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x150c80f690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This should really be -inf to positive inf, but graph can only be so big. \n",
    "# Currently it is plus or minus 5 std deviations \n",
    "a, b = 1, 2 # integral limits\n",
    "\n",
    "x = np.linspace(-4, 4)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(1.5, .02, r'{0:.2f}%'.format(result*100),\n",
    "         horizontalalignment='center', fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (Mean + 2STD) to (Mean + 3STD)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result, error = quad(normalProbabilityDensity, 2, 3, limit = 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02140023391654912"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ExmRu3ry5GA8tEhumT59Ox446ECzRS9NHiBQtmNJV2K/exbm8/PHOuQygBzDG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\nLhEREZEw+H+CofYbsvwxagAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x150d14ecd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This should really be -inf to positive inf, but graph can only be so big. \n",
    "# Currently it is plus or minus 5 std deviations \n",
    "a, b = 2, 3 # integral limits\n",
    "\n",
    "x = np.linspace(-4, 4)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "#ax.text(1.5, .02, r'{0:.1f}%'.format(result*100),\n",
    "#         horizontalalignment='center', fontsize=15);\n",
    "\n",
    "ax.annotate(r'{0:.2f}%'.format(result*100),\n",
    "            xy=(2.5, 0.001), xycoords='data',\n",
    "            xytext=(2.5, 0.05), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"-\",\n",
    "                            connectionstyle=\"arc3\"),\n",
    "            );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (Mean + 3STD) to (Mean + 4STD)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result, error = quad(normalProbabilityDensity, 3, 4, limit = 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0013182267897969746"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uwDVatwIzgCxgknNukZndb2Y/X1X3AlDdzJYDg4Gfp5VoCywws/kU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\nPDenSvGyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x150d1dca10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This should really be -inf to positive inf, but graph can only be so big. \n",
    "# Currently it is plus or minus 5 std deviations \n",
    "a, b = 3, 4 # integral limits\n",
    "\n",
    "x = np.linspace(-4, 4)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.annotate(r'{0:.2f}%'.format(result*100),\n",
    "            xy=(3.3, 0.001), xycoords='data',\n",
    "            xytext=(3.2, 0.05), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"-\",\n",
    "                            connectionstyle=\"arc3\"),\n",
    "            );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean + 4STD (4) to Infinity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the area under the curve that wont fit in my picture. Notice the probability is so small"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result, error = quad(normalProbabilityDensity, 4, np.inf, limit = 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.1671241830206856e-05"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lets put together the Entire Graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you think this is too much code, next section will make this better. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Area under curve for entire Graph\n",
    "result, _ = quad(normalProbabilityDensity, np.NINF, np.inf)\n",
    "\n",
    "# Integrate normal distribution from 0 to 1\n",
    "result_0_1, _ = quad(normalProbabilityDensity, 0, 1, limit = 1000)\n",
    "\n",
    "# Integrate normal distribution from -1 to 0\n",
    "result_n1_0, _ = quad(normalProbabilityDensity, -1, 0, limit = 1000)\n",
    "\n",
    "# Integrate normal distribution from 1 to 2\n",
    "result_1_2, _ = quad(normalProbabilityDensity, 1, 2, limit = 1000)\n",
    "\n",
    "# Integrate normal distribution from -2 to -1\n",
    "result_n2_n1, _ = quad(normalProbabilityDensity, -2, -1, limit = 1000)\n",
    "\n",
    "# Integrate normal distribution from 2 to 3\n",
    "result_2_3, _ = quad(normalProbabilityDensity, 2, 3, limit = 1000)\n",
    "\n",
    "# Integrate normal distribution from -3 to -2\n",
    "result_n3_n2, _ = quad(normalProbabilityDensity, -3, -2, limit = 1000)\n",
    "\n",
    "# Integrate normal distribution from 3 to 4\n",
    "result_3_4, _ = quad(normalProbabilityDensity, 3, 4, limit = 1000)\n",
    "\n",
    "# Integrate normal distribution from -4 to -3\n",
    "result_n4_n3, _ = quad(normalProbabilityDensity, -4, -3, limit = 1000)\n",
    "\n",
    "# Integrate normal distribution from 4 to inf\n",
    "result_4_inf, error = quad(normalProbabilityDensity, 4, np.inf, limit = 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ShCmTJ3Pu+edHHUdEdlORBaC7zynudRJcAbQC2rn7IgAz+wT4mmCqmSKvNnb3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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x150d651090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This should really be -inf to positive inf, but graph can only be so big. \n",
    "# Currently it is plus or minus 5 std deviations \n",
    "\n",
    "x = np.linspace(-4, 4)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "#############################\n",
    "a, b = 0, 1 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(0, 1)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(0.5, .04, r'{0:.2f}%'.format(result_0_1*100),\n",
    "         horizontalalignment='center', fontsize=14);\n",
    "\n",
    "##############################\n",
    "a, b = -1, 0 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(-1, 0)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(-0.5, .04, r'{0:.2f}%'.format(result_n1_0*100),\n",
    "         horizontalalignment='center', fontsize=14);\n",
    "\n",
    "##############################\n",
    "a, b = 1, 2 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(1, 2)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='blue', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(1.5, .04, r'{0:.2f}%'.format(result_1_2*100),\n",
    "         horizontalalignment='center', fontsize=14);\n",
    "\n",
    "##############################\n",
    "a, b = -2, -1 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(-2, -1)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='blue', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(-1.5, .04, r'{0:.2f}%'.format(result_n2_n1*100),\n",
    "         horizontalalignment='center', fontsize=14);\n",
    "\n",
    "##############################\n",
    "a, b = 2, 3 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(2, 3)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='green', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(2.6, .04, r'{0:.2f}%'.format(result_2_3*100),\n",
    "         horizontalalignment='center', fontsize=14);\n",
    "\n",
    "\n",
    "##############################\n",
    "a, b = -3, -2 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(-3, -2)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='green', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(-2.6, .04, r'{0:.2f}%'.format(result_2_3*100),\n",
    "         horizontalalignment='center', fontsize=14);\n",
    "\n",
    "##############################\n",
    "a, b = 3, 4 # integral limits\n",
    "\n",
    "# Region from 3 to 4\n",
    "ix = np.linspace(3, 4)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(3, 0)] + list(zip(ix, iy)) + [(4, 0)]\n",
    "poly = Polygon(verts, facecolor='orange', edgecolor='.2', alpha = 1)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(3.6, .04, r'{0:.2f}%'.format(result_3_4*100),\n",
    "         horizontalalignment='center', fontsize=14);\n",
    "\n",
    "# Region from -4 to -3\n",
    "ix = np.linspace(-4, -3)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(-4, 0)] + list(zip(ix, iy)) + [(-3, 0)]\n",
    "poly = Polygon(verts, facecolor='orange', edgecolor='.2', alpha = 1)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(-3.6, .040, r'{0:.2f}%'.format(result_n4_n3*100),\n",
    "         horizontalalignment='center', fontsize=14);\n",
    "\n",
    "ax.set_title(r'Normal Distribution', fontsize = 24)\n",
    "ax.set_ylabel(r'Probability Density', fontsize = 18)\n",
    "\n",
    "xTickLabels = ['',\n",
    "               r'$\\mu - 4\\sigma$',\n",
    "               r'$\\mu - 3\\sigma$',\n",
    "               r'$\\mu - 2\\sigma$',\n",
    "               r'$\\mu - \\sigma$',\n",
    "               r'$\\mu$',\n",
    "               r'$\\mu + \\sigma$',\n",
    "               r'$\\mu + 2\\sigma$',\n",
    "               r'$\\mu + 3\\sigma$',\n",
    "               r'$\\mu + 4\\sigma$']\n",
    "\n",
    "yTickLabels = ['0.00',\n",
    "               '0.05',\n",
    "               '0.10',\n",
    "               '0.15',\n",
    "               '0.20',\n",
    "               '0.25',\n",
    "               '0.30',\n",
    "               '0.35',\n",
    "               '0.40']\n",
    "\n",
    "ax.set_xticklabels(xTickLabels, fontsize = 16)\n",
    "\n",
    "ax.set_yticklabels(yTickLabels, fontsize = 16)\n",
    "\n",
    "fig.savefig('images/NormalDistribution.png', dpi = 1200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 68-95-99.7 Rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most people commonly associate the normal distribution with the 68-95-99.7 rule where 68% of the data is within 1 standard deviation (σ) of the mean (μ), 95% of the data is within 2 standard deviations (σ) of the mean  (μ), and 99.7% of the data is within 3 standard deviations (σ) of the mean  (μ). The graph below shows that. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zLxcrHhFB90sv5eURIxj0wgteh2OM8SPNBBDoAgxyv1bgPvfw5wjwaBbFZYwJ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\nLSlTuZzd4SilVKHXrHcz9iXtY8DAARw9etTucJSX2T0NTHZTkEsejpO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      "text/plain": [
       "<matplotlib.figure.Figure at 0x150d4d2b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This should really be -inf to positive inf, but graph can only be so big. \n",
    "# Currently it is plus or minus 5 std deviations \n",
    "\n",
    "x = np.linspace(-3, 3)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "#############################\n",
    "a, b = -1, 1 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(-1, 1)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(0.0, .28, r'{0:.2f}%'.format((result_n1_0 + result_0_1)*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "# Bounding the make arrow \n",
    "ax.annotate(r'',\n",
    "            xy=(-1, .27), xycoords='data',\n",
    "            xytext=(1, .27), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "##############################\n",
    "a, b = 1, 2 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(1, 2)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='blue', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "##############################\n",
    "a, b = -2, -1 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(-2, -1)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='blue', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "#ax.text(-1.5, .04, r'{0:.2f}%'.format(result_n2_n1*100),\n",
    "#         horizontalalignment='center', fontsize=14);\n",
    "\n",
    "ax.text(0.0, .18, r'{0:.2f}%'.format((result_n2_n1 + result_n1_0 + result_0_1 + result_1_2)*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "# Bounding the make arrow \n",
    "ax.annotate(r'',\n",
    "            xy=(-2, .17), xycoords='data',\n",
    "            xytext=(2, .17), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "##############################\n",
    "a, b = 2, 3 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(2, 3)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='green', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "##############################\n",
    "a, b = -3, -2 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(-3, -2)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='green', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "### This is the middle part\n",
    "ax.text(0.0, .08, r'{0:.2f}%'.format((result_n3_n2 + result_n2_n1 + result_n1_0 + result_0_1 + result_1_2 + result_2_3)*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "# Bounding the make arrow \n",
    "ax.annotate(r'',\n",
    "            xy=(-3, .07), xycoords='data',\n",
    "            xytext=(3, .07), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "ax.set_title(r'68-95-99.7 Rule', fontsize = 24)\n",
    "ax.set_ylabel(r'Probability Density', fontsize = 18)\n",
    "\n",
    "xTickLabels = ['',\n",
    "               r'$\\mu - 3\\sigma$',\n",
    "               r'$\\mu - 2\\sigma$',\n",
    "               r'$\\mu - \\sigma$',\n",
    "               r'$\\mu$',\n",
    "               r'$\\mu + \\sigma$',\n",
    "               r'$\\mu + 2\\sigma$',\n",
    "               r'$\\mu + 3\\sigma$']\n",
    "\n",
    "yTickLabels = ['0.00',\n",
    "               '0.05',\n",
    "               '0.10',\n",
    "               '0.15',\n",
    "               '0.20',\n",
    "               '0.25',\n",
    "               '0.30',\n",
    "               '0.35',\n",
    "               '0.40']\n",
    "\n",
    "ax.set_xticklabels(xTickLabels, fontsize = 16)\n",
    "\n",
    "ax.set_yticklabels(yTickLabels, fontsize = 16)\n",
    "\n",
    "fig.savefig('images/68_95_99_rule.png', dpi = 1200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normal Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('mean: ', 0)\n",
      "('std: ', 0)\n"
     ]
    }
   ],
   "source": [
    "# Draw samples from normal distribution\n",
    "# Mean is 0 \n",
    "# Std is 1\n",
    "mu, sigma = 0, 1\n",
    "\n",
    "myNormalDistribution = np.random.normal(mu, sigma,  100000000)\n",
    "\n",
    "# Mean is close to Zero\n",
    "mean = myNormalDistribution.mean()\n",
    "standardDeviation = myNormalDistribution.std()\n",
    "print('mean: ', int(mean))\n",
    "\n",
    "# Standard deviation and variance is 1\n",
    "print('std: ', int(standardDeviation))\n",
    "\n",
    "## Show new graph with mean 0 and standard deviation of 1 \n",
    "## because needed for showing how z table is calculated and show new graph\n",
    "## before integrating. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Generate the Z-Score Table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Need to look up pretty looking tables and make one myself using integrals and show it finally in pandas arrays. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://en.wikipedia.org/wiki/Standard_normal_table \n",
    "\n",
    "Mention https://en.wikipedia.org/wiki/68–95–99.7_rule somewhere in article about it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      0    1    2    3    4    5    6    7    8    9\n",
       "0   0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n",
       "1   0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n",
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       "39  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data = np.zeros((40, 10)), columns = np.li )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "401"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(np.linspace(.00, 4, num = 401))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
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      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(401)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "standardNormalTable = [np.nan] * 40001\n",
    "\n",
    "for index, upperLimit in enumerate(np.linspace(.00, 4, num = 40001)):\n",
    "    result, _ = quad(normalProbabilityDensity, 0, upperLimit, limit = 1000)\n",
    "    standardNormalTable[index] = [upperLimit, result]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "      <th>0</th>\n",
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       "      <td>0.0008</td>\n",
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       "      <th>12</th>\n",
       "      <td>0.0012</td>\n",
       "      <td>0.000479</td>\n",
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       "      <td>0.0017</td>\n",
       "      <td>0.000678</td>\n",
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       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.0018</td>\n",
       "      <td>0.000718</td>\n",
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       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.0019</td>\n",
       "      <td>0.000758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.0020</td>\n",
       "      <td>0.000798</td>\n",
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       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.0021</td>\n",
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       "      <td>0.0022</td>\n",
       "      <td>0.000878</td>\n",
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       "      <th>23</th>\n",
       "      <td>0.0023</td>\n",
       "      <td>0.000918</td>\n",
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       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.0024</td>\n",
       "      <td>0.000957</td>\n",
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       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.0025</td>\n",
       "      <td>0.000997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.0026</td>\n",
       "      <td>0.001037</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.0027</td>\n",
       "      <td>0.001077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.0028</td>\n",
       "      <td>0.001117</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.0029</td>\n",
       "      <td>0.001157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39971</th>\n",
       "      <td>3.9971</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39972</th>\n",
       "      <td>3.9972</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39973</th>\n",
       "      <td>3.9973</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39974</th>\n",
       "      <td>3.9974</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39975</th>\n",
       "      <td>3.9975</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39976</th>\n",
       "      <td>3.9976</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39977</th>\n",
       "      <td>3.9977</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39978</th>\n",
       "      <td>3.9978</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39979</th>\n",
       "      <td>3.9979</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39980</th>\n",
       "      <td>3.9980</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39981</th>\n",
       "      <td>3.9981</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39982</th>\n",
       "      <td>3.9982</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39983</th>\n",
       "      <td>3.9983</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39984</th>\n",
       "      <td>3.9984</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39985</th>\n",
       "      <td>3.9985</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39986</th>\n",
       "      <td>3.9986</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39987</th>\n",
       "      <td>3.9987</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39988</th>\n",
       "      <td>3.9988</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39989</th>\n",
       "      <td>3.9989</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39990</th>\n",
       "      <td>3.9990</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39991</th>\n",
       "      <td>3.9991</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39992</th>\n",
       "      <td>3.9992</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39993</th>\n",
       "      <td>3.9993</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39994</th>\n",
       "      <td>3.9994</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39995</th>\n",
       "      <td>3.9995</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39996</th>\n",
       "      <td>3.9996</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39997</th>\n",
       "      <td>3.9997</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39998</th>\n",
       "      <td>3.9998</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39999</th>\n",
       "      <td>3.9999</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40000</th>\n",
       "      <td>4.0000</td>\n",
       "      <td>0.499968</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>40001 rows × 2 columns</p>\n",
       "</div>"
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       "            0         1\n",
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       "3      0.0003  0.000120\n",
       "4      0.0004  0.000160\n",
       "5      0.0005  0.000199\n",
       "6      0.0006  0.000239\n",
       "7      0.0007  0.000279\n",
       "8      0.0008  0.000319\n",
       "9      0.0009  0.000359\n",
       "10     0.0010  0.000399\n",
       "11     0.0011  0.000439\n",
       "12     0.0012  0.000479\n",
       "13     0.0013  0.000519\n",
       "14     0.0014  0.000559\n",
       "15     0.0015  0.000598\n",
       "16     0.0016  0.000638\n",
       "17     0.0017  0.000678\n",
       "18     0.0018  0.000718\n",
       "19     0.0019  0.000758\n",
       "20     0.0020  0.000798\n",
       "21     0.0021  0.000838\n",
       "22     0.0022  0.000878\n",
       "23     0.0023  0.000918\n",
       "24     0.0024  0.000957\n",
       "25     0.0025  0.000997\n",
       "26     0.0026  0.001037\n",
       "27     0.0027  0.001077\n",
       "28     0.0028  0.001117\n",
       "29     0.0029  0.001157\n",
       "...       ...       ...\n",
       "39971  3.9971  0.499968\n",
       "39972  3.9972  0.499968\n",
       "39973  3.9973  0.499968\n",
       "39974  3.9974  0.499968\n",
       "39975  3.9975  0.499968\n",
       "39976  3.9976  0.499968\n",
       "39977  3.9977  0.499968\n",
       "39978  3.9978  0.499968\n",
       "39979  3.9979  0.499968\n",
       "39980  3.9980  0.499968\n",
       "39981  3.9981  0.499968\n",
       "39982  3.9982  0.499968\n",
       "39983  3.9983  0.499968\n",
       "39984  3.9984  0.499968\n",
       "39985  3.9985  0.499968\n",
       "39986  3.9986  0.499968\n",
       "39987  3.9987  0.499968\n",
       "39988  3.9988  0.499968\n",
       "39989  3.9989  0.499968\n",
       "39990  3.9990  0.499968\n",
       "39991  3.9991  0.499968\n",
       "39992  3.9992  0.499968\n",
       "39993  3.9993  0.499968\n",
       "39994  3.9994  0.499968\n",
       "39995  3.9995  0.499968\n",
       "39996  3.9996  0.499968\n",
       "39997  3.9997  0.499968\n",
       "39998  3.9998  0.499968\n",
       "39999  3.9999  0.499968\n",
       "40000  4.0000  0.499968\n",
       "\n",
       "[40001 rows x 2 columns]"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data = standardNormalTable)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4001"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(.00, 4, num = 4001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 77 µs, sys: 11 µs, total: 88 µs\n",
      "Wall time: 83.2 µs\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0.  , 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 ,\n",
       "       0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21,\n",
       "       0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31, 0.32,\n",
       "       0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42, 0.43,\n",
       "       0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5 , 0.51, 0.52, 0.53, 0.54,\n",
       "       0.55, 0.56, 0.57, 0.58, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64, 0.65,\n",
       "       0.66, 0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75, 0.76,\n",
       "       0.77, 0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87,\n",
       "       0.88, 0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98,\n",
       "       0.99, 1.  , 1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, 1.09,\n",
       "       1.1 , 1.11, 1.12, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18, 1.19, 1.2 ,\n",
       "       1.21, 1.22, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, 1.29, 1.3 , 1.31,\n",
       "       1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38, 1.39, 1.4 , 1.41, 1.42,\n",
       "       1.43, 1.44, 1.45, 1.46, 1.47, 1.48, 1.49, 1.5 , 1.51, 1.52, 1.53,\n",
       "       1.54, 1.55, 1.56, 1.57, 1.58, 1.59, 1.6 , 1.61, 1.62, 1.63, 1.64,\n",
       "       1.65, 1.66, 1.67, 1.68, 1.69, 1.7 , 1.71, 1.72, 1.73, 1.74, 1.75,\n",
       "       1.76, 1.77, 1.78, 1.79, 1.8 , 1.81, 1.82, 1.83, 1.84, 1.85, 1.86,\n",
       "       1.87, 1.88, 1.89, 1.9 , 1.91, 1.92, 1.93, 1.94, 1.95, 1.96, 1.97,\n",
       "       1.98, 1.99, 2.  , 2.01, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08,\n",
       "       2.09, 2.1 , 2.11, 2.12, 2.13, 2.14, 2.15, 2.16, 2.17, 2.18, 2.19,\n",
       "       2.2 , 2.21, 2.22, 2.23, 2.24, 2.25, 2.26, 2.27, 2.28, 2.29, 2.3 ,\n",
       "       2.31, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, 2.39, 2.4 , 2.41,\n",
       "       2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, 2.49, 2.5 , 2.51, 2.52,\n",
       "       2.53, 2.54, 2.55, 2.56, 2.57, 2.58, 2.59, 2.6 , 2.61, 2.62, 2.63,\n",
       "       2.64, 2.65, 2.66, 2.67, 2.68, 2.69, 2.7 , 2.71, 2.72, 2.73, 2.74,\n",
       "       2.75, 2.76, 2.77, 2.78, 2.79, 2.8 , 2.81, 2.82, 2.83, 2.84, 2.85,\n",
       "       2.86, 2.87, 2.88, 2.89, 2.9 , 2.91, 2.92, 2.93, 2.94, 2.95, 2.96,\n",
       "       2.97, 2.98, 2.99, 3.  , 3.01, 3.02, 3.03, 3.04, 3.05, 3.06, 3.07,\n",
       "       3.08, 3.09, 3.1 , 3.11, 3.12, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18,\n",
       "       3.19, 3.2 , 3.21, 3.22, 3.23, 3.24, 3.25, 3.26, 3.27, 3.28, 3.29,\n",
       "       3.3 , 3.31, 3.32, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, 3.39, 3.4 ,\n",
       "       3.41, 3.42, 3.43, 3.44, 3.45, 3.46, 3.47, 3.48, 3.49, 3.5 , 3.51,\n",
       "       3.52, 3.53, 3.54, 3.55, 3.56, 3.57, 3.58, 3.59, 3.6 , 3.61, 3.62,\n",
       "       3.63, 3.64, 3.65, 3.66, 3.67, 3.68, 3.69, 3.7 , 3.71, 3.72, 3.73,\n",
       "       3.74, 3.75, 3.76, 3.77, 3.78, 3.79, 3.8 , 3.81, 3.82, 3.83, 3.84,\n",
       "       3.85, 3.86, 3.87, 3.88, 3.89, 3.9 , 3.91, 3.92, 3.93, 3.94, 3.95,\n",
       "       3.96, 3.97, 3.98, 3.99, 4.  ])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "# Mention how slow this is\n",
    "\n",
    "\n",
    "\n",
    "# Integrate normal distribution from 0 to 1\n",
    "result_0_1, _ = quad(normalProbabilityDensity, 0, 1, limit = 1000)\n",
    "\n",
    "\n",
    "np.linspace(.00, 4, num = 401)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 0 to something. \n",
    "\n",
    "# Integrate normal distribution from 0 to 1\n",
    "\n",
    "\n",
    "for \n",
    "result_0_1, _ = quad(normalProbabilityDensity, 0, 1, limit = 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now lets look at Box Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stack Overflow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Good Explanation of probability density function: https://math.stackexchange.com/questions/2095323/probability-density-function-graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://math.stackexchange.com/questions/1394789/how-to-calculate-probability-with-z-score-not-on-table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "normal distribution: https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.normal.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "python area under the curve: https://matplotlib.org/gallery/showcase/integral.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "something similar to this in R: https://qualityandinnovation.com/2017/02/02/where-do-z-score-tables-come-from-how-to-make-them-in-r/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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